Semiconductor devices such as logic and memory devices are typically fabricated by a sequence of processing steps applied to a specimen. The various features and multiple structural levels of the semiconductor devices are formed by these processing steps. For example, lithography among others is one semiconductor fabrication process that involves generating a pattern on a semiconductor wafer. Additional examples of semiconductor fabrication processes include, but are not limited to, chemical-mechanical polishing, etch, deposition, and ion implantation. Multiple semiconductor devices may be fabricated on a single semiconductor wafer and then separated into individual semiconductor devices.
Metrology processes are used at various steps during a semiconductor manufacturing process to detect defects on wafers to promote higher yield. Model-based metrology techniques offer the potential for high throughput without the risk of sample destruction. A number of model-based metrology based techniques including scatterometry, ellipsometry, and reflectometry implementations and associated analysis algorithms are commonly used to characterize critical dimensions, film thicknesses, composition, overlay and other parameters of nanoscale structures.
Modern semiconductor processes are employed to produce complex structures. A complex measurement model with multiple parameters is required to represent these structures and account for process and dimensional variations. Complex, multiple parameter models include modeling errors induced by parameter correlations and low measurement sensitivity to some parameters. In addition, regression of complex, multiple parameter models having a relatively large number of floating parameter values may not be computationally tractable.
To reduce the impact of these error sources and reduce computational effort, a number of parameters are typically fixed in a model-based measurement. Although fixing the values of a number of parameters may improve calculation speed and reduce the impact of parameter correlations, it also leads to errors in the estimates of parameter values.
Currently, the solution of complex, multiple parameter measurement models often requires an unsatisfactory compromise. Current model reduction techniques are sometimes unable to arrive at a measurement model that is both computationally tractable and sufficiently accurate. Moreover, complex, multiple parameter models make it difficult, or impossible, to optimize system parameter selections (e.g., wavelengths, angles of incidence, etc.) for each parameter of interest.
Future metrology applications present challenges due to increasingly small resolution requirements, multi-parameter correlation, increasingly complex geometric structures, and increasing use of opaque materials. Thus, methods and systems for improved measurements are desired.